Space of modular forms of level 127, weight 2, and trivial character

• Label: 127.2.a
• Level: $127$
• Weight: $2$
• Character orbit: 127.a
• Rep. character: $\chi_{127}(1,\cdot)$
• Character field: $\Q$
• Dimension: $10$
• Newform subspaces: $2$
• Sturm bound: $21$
• Trace bound: $1$

Defining parameters

Level:	\( N \)	\(=\)	\( 127 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	127.a (trivial)
Character field:			\(\Q\)
Newform subspaces:			\( 2 \)
Sturm bound:			\(21\)
Trace bound:			\(1\)
Distinguishing \(T_p\):			\(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(127))\).

	Total	New	Old
Modular forms	11	11	0
Cusp forms	10	10	0
Eisenstein series	1	1	0

The following table gives the dimensions of the cuspidal new subspaces with specified eigenvalues for the Atkin-Lehner operators and the Fricke involution.

\(127\)		Total				Cusp				Eisenstein
		All	New	Old		All	New	Old		All	New	Old
\(+\)		\(3\)	\(3\)	\(0\)		\(3\)	\(3\)	\(0\)		\(0\)	\(0\)	\(0\)
\(-\)		\(8\)	\(8\)	\(0\)		\(7\)	\(7\)	\(0\)		\(1\)	\(1\)	\(0\)

Trace form

10 * q - q^2 + 9 * q^4 + 2 * q^5 - 6 * q^6 - 6 * q^7 - 3 * q^8 + 12 * q^9 - 2 * q^10 - 4 * q^12 - 4 * q^13 - 4 * q^14 - 6 * q^15 - 5 * q^16 + 6 * q^17 + 3 * q^18 - 2 * q^19 + 14 * q^20 - 16 * q^21 + 6 * q^22 - 10 * q^23 - 6 * q^24 + 10 * q^25 + 2 * q^26 - 20 * q^28 - 4 * q^29 - 34 * q^30 + 4 * q^31 - 2 * q^32 - 2 * q^33 + 11 * q^34 + 16 * q^35 + q^36 - 6 * q^37 + 23 * q^38 - 6 * q^40 + 2 * q^41 + 18 * q^42 - 10 * q^43 - 39 * q^44 + 16 * q^45 + 6 * q^46 + 22 * q^47 - 10 * q^48 - 12 * q^49 + 13 * q^50 + 38 * q^51 - 15 * q^52 + 32 * q^53 - 8 * q^54 - 26 * q^55 - 2 * q^57 - 40 * q^58 - 12 * q^59 + 4 * q^61 - 11 * q^62 - 4 * q^63 + 9 * q^64 - 6 * q^65 + 18 * q^66 - 28 * q^67 + 44 * q^68 + 24 * q^69 + 42 * q^70 + 10 * q^71 - 37 * q^72 + 16 * q^73 + 35 * q^74 + 12 * q^75 + 24 * q^76 + 16 * q^77 + 20 * q^78 - 14 * q^79 - 2 * q^80 - 14 * q^81 + 26 * q^82 + 38 * q^83 - 50 * q^84 + 54 * q^85 - 4 * q^86 - 20 * q^87 + 19 * q^88 - 20 * q^89 - 42 * q^90 - 52 * q^91 - 50 * q^92 - 4 * q^93 + 14 * q^94 - 40 * q^95 + 46 * q^96 - 20 * q^97 + q^98 - 2 * q^99

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(127))\) into newform subspaces

Label	Level	Weight	Char	Prim	Char order	Dim	Rel. Dim	$A$	Field	CM	Self-dual	Twist minimal	Largest	Maximal	Minimal twist	Inner twists	Rank*	Traces					A-L signs	Fricke sign	Coefficient ring index	Sato-Tate	$q$-expansion
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$		127
127.2.a.a	$127$	$2$	127.a	1.a	$1$	$3$	$3$	$1.014$	\(\Q(\zeta_{18})^+\)	None	✓	✓	✓	✓	127.2.a.a	$1$	$1$	\(-3\)	\(-3\)	\(-6\)	\(-3\)		$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q+(-1+\beta _{1})q^{2}+(-1-\beta _{2})q^{3}+(1+\cdots)q^{4}+\cdots\)
127.2.a.b	$127$	$2$	127.a	1.a	$1$	$7$	$7$	$1.014$	\(\mathbb{Q}[x]/(x^{7} - \cdots)\)	None	✓	✓	✓	✓	127.2.a.b	$1$	$0$	\(2\)	\(3\)	\(8\)	\(-3\)		$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+\beta _{1}q^{2}+(1-\beta _{2}+\beta _{3}+\beta _{5}+\beta _{6})q^{3}+\cdots\)